In [23] M. Pierre introduced parabolic Dirichlet spaces. Such spaces are obtained by considering certain families ${\left(E^{\left(\tau \right)}\right)}_{\tau \in ℝ}$ of Dirichlet forms. He developed a rather far-reaching and general potential theory for these spaces. In particular, he introduced associated capacities and investigated the notion of related quasi-continuous functions. However, the only examples given by M. Pierre in [23] (see also [22]) are Dirichlet forms arising from strongly parabolic differential operators of second order. To...